Beat all of the version 1 bosses, and get rewarded a black boss chest (no spells or rings because that would pretty much defeat the game mode if you get freeze spell or OP rings). Getting a black chest ensures you get armor or a decent weapon.

Next you fight all the version 2 bosses (coral riff 2, FM2, king conga 2 etc) randomly. Once they're all defeated, you get another black boss chest.

Eventually once you get passed the version 5 bosses, you'll get a choice between one of the 3 boss chests (to help with your story boss). If you don't have a story boss then the run will end and you win.